Pat chicken thighs dry and season with salt, black pepper, ground mustard, paprika and garlic on both sides. Gently rub it into the chicken and allow it to sit for 15-30 minutes if possible.
Heat 1 tablespoon olive oil over skillet preheated to medium high heat. Place chicken in hot oil and allow to sear for 3-4 minutes per side. Chicken will start to pull away from the pan when ready to flip.
Remove the chicken from the skillet and set aside. (It will not be fully cooked at this time, and that is ok!) Add another tablespoon of olive oil and add the onion to hot oil, sautéing for 2-3 minutes. Add the Brussels sprouts and try to shake skillet to allow as many sprouts as possible to be cut side down. Don't touch them for about 4-5 minutes or until they start to get golden brown and crisp. Stir, sprinkle with salt, pepper and garlic as desired and allow to cook for another 2- 3 minutes.
While the sprouts cook, whisk together the chicken stock, balsamic vinegar, dijon mustard, and garlic. Add the chicken back into the skillet, pour the balsamic mixture over top. Cover the pan and allow to simmer for about 7-10 minutes more or until the chicken reaches 170°F-175°F internal temperature and sauce has slightly reduced.
Remove from the stove, allow to rest for 5 minutes for juiciest chicken. Sprinkle with goat cheese and pomegranate arils and serve!